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LAPACK 3.3.1
Linear Algebra PACKage
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LAPACK 3.3.1
Linear Algebra PACKage
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00001 SUBROUTINE SGBSVXX( FACT, TRANS, N, KL, KU, NRHS, AB, LDAB, AFB, 00002 $ LDAFB, IPIV, EQUED, R, C, B, LDB, X, LDX, 00003 $ RCOND, RPVGRW, BERR, N_ERR_BNDS, 00004 $ ERR_BNDS_NORM, ERR_BNDS_COMP, NPARAMS, PARAMS, 00005 $ WORK, IWORK, INFO ) 00006 * 00007 * -- LAPACK driver routine (version 3.2) -- 00008 * -- Contributed by James Demmel, Deaglan Halligan, Yozo Hida and -- 00009 * -- Jason Riedy of Univ. of California Berkeley. -- 00010 * -- November 2008 -- 00011 * 00012 * -- LAPACK is a software package provided by Univ. of Tennessee, -- 00013 * -- Univ. of California Berkeley and NAG Ltd. -- 00014 * 00015 IMPLICIT NONE 00016 * .. 00017 * .. Scalar Arguments .. 00018 CHARACTER EQUED, FACT, TRANS 00019 INTEGER INFO, LDAB, LDAFB, LDB, LDX, N, NRHS, NPARAMS, 00020 $ N_ERR_BNDS 00021 REAL RCOND, RPVGRW 00022 * .. 00023 * .. Array Arguments .. 00024 INTEGER IPIV( * ), IWORK( * ) 00025 REAL AB( LDAB, * ), AFB( LDAFB, * ), B( LDB, * ), 00026 $ X( LDX , * ),WORK( * ) 00027 REAL R( * ), C( * ), PARAMS( * ), BERR( * ), 00028 $ ERR_BNDS_NORM( NRHS, * ), 00029 $ ERR_BNDS_COMP( NRHS, * ) 00030 * .. 00031 * 00032 * Purpose 00033 * ======= 00034 * 00035 * SGBSVXX uses the LU factorization to compute the solution to a 00036 * real system of linear equations A * X = B, where A is an 00037 * N-by-N matrix and X and B are N-by-NRHS matrices. 00038 * 00039 * If requested, both normwise and maximum componentwise error bounds 00040 * are returned. SGBSVXX will return a solution with a tiny 00041 * guaranteed error (O(eps) where eps is the working machine 00042 * precision) unless the matrix is very ill-conditioned, in which 00043 * case a warning is returned. Relevant condition numbers also are 00044 * calculated and returned. 00045 * 00046 * SGBSVXX accepts user-provided factorizations and equilibration 00047 * factors; see the definitions of the FACT and EQUED options. 00048 * Solving with refinement and using a factorization from a previous 00049 * SGBSVXX call will also produce a solution with either O(eps) 00050 * errors or warnings, but we cannot make that claim for general 00051 * user-provided factorizations and equilibration factors if they 00052 * differ from what SGBSVXX would itself produce. 00053 * 00054 * Description 00055 * =========== 00056 * 00057 * The following steps are performed: 00058 * 00059 * 1. If FACT = 'E', real scaling factors are computed to equilibrate 00060 * the system: 00061 * 00062 * TRANS = 'N': diag(R)*A*diag(C) *inv(diag(C))*X = diag(R)*B 00063 * TRANS = 'T': (diag(R)*A*diag(C))**T *inv(diag(R))*X = diag(C)*B 00064 * TRANS = 'C': (diag(R)*A*diag(C))**H *inv(diag(R))*X = diag(C)*B 00065 * 00066 * Whether or not the system will be equilibrated depends on the 00067 * scaling of the matrix A, but if equilibration is used, A is 00068 * overwritten by diag(R)*A*diag(C) and B by diag(R)*B (if TRANS='N') 00069 * or diag(C)*B (if TRANS = 'T' or 'C'). 00070 * 00071 * 2. If FACT = 'N' or 'E', the LU decomposition is used to factor 00072 * the matrix A (after equilibration if FACT = 'E') as 00073 * 00074 * A = P * L * U, 00075 * 00076 * where P is a permutation matrix, L is a unit lower triangular 00077 * matrix, and U is upper triangular. 00078 * 00079 * 3. If some U(i,i)=0, so that U is exactly singular, then the 00080 * routine returns with INFO = i. Otherwise, the factored form of A 00081 * is used to estimate the condition number of the matrix A (see 00082 * argument RCOND). If the reciprocal of the condition number is less 00083 * than machine precision, the routine still goes on to solve for X 00084 * and compute error bounds as described below. 00085 * 00086 * 4. The system of equations is solved for X using the factored form 00087 * of A. 00088 * 00089 * 5. By default (unless PARAMS(LA_LINRX_ITREF_I) is set to zero), 00090 * the routine will use iterative refinement to try to get a small 00091 * error and error bounds. Refinement calculates the residual to at 00092 * least twice the working precision. 00093 * 00094 * 6. If equilibration was used, the matrix X is premultiplied by 00095 * diag(C) (if TRANS = 'N') or diag(R) (if TRANS = 'T' or 'C') so 00096 * that it solves the original system before equilibration. 00097 * 00098 * Arguments 00099 * ========= 00100 * 00101 * Some optional parameters are bundled in the PARAMS array. These 00102 * settings determine how refinement is performed, but often the 00103 * defaults are acceptable. If the defaults are acceptable, users 00104 * can pass NPARAMS = 0 which prevents the source code from accessing 00105 * the PARAMS argument. 00106 * 00107 * FACT (input) CHARACTER*1 00108 * Specifies whether or not the factored form of the matrix A is 00109 * supplied on entry, and if not, whether the matrix A should be 00110 * equilibrated before it is factored. 00111 * = 'F': On entry, AF and IPIV contain the factored form of A. 00112 * If EQUED is not 'N', the matrix A has been 00113 * equilibrated with scaling factors given by R and C. 00114 * A, AF, and IPIV are not modified. 00115 * = 'N': The matrix A will be copied to AF and factored. 00116 * = 'E': The matrix A will be equilibrated if necessary, then 00117 * copied to AF and factored. 00118 * 00119 * TRANS (input) CHARACTER*1 00120 * Specifies the form of the system of equations: 00121 * = 'N': A * X = B (No transpose) 00122 * = 'T': A**T * X = B (Transpose) 00123 * = 'C': A**H * X = B (Conjugate Transpose = Transpose) 00124 * 00125 * N (input) INTEGER 00126 * The number of linear equations, i.e., the order of the 00127 * matrix A. N >= 0. 00128 * 00129 * KL (input) INTEGER 00130 * The number of subdiagonals within the band of A. KL >= 0. 00131 * 00132 * KU (input) INTEGER 00133 * The number of superdiagonals within the band of A. KU >= 0. 00134 * 00135 * NRHS (input) INTEGER 00136 * The number of right hand sides, i.e., the number of columns 00137 * of the matrices B and X. NRHS >= 0. 00138 * 00139 * AB (input/output) REAL array, dimension (LDAB,N) 00140 * On entry, the matrix A in band storage, in rows 1 to KL+KU+1. 00141 * The j-th column of A is stored in the j-th column of the 00142 * array AB as follows: 00143 * AB(KU+1+i-j,j) = A(i,j) for max(1,j-KU)<=i<=min(N,j+kl) 00144 * 00145 * If FACT = 'F' and EQUED is not 'N', then AB must have been 00146 * equilibrated by the scaling factors in R and/or C. AB is not 00147 * modified if FACT = 'F' or 'N', or if FACT = 'E' and 00148 * EQUED = 'N' on exit. 00149 * 00150 * On exit, if EQUED .ne. 'N', A is scaled as follows: 00151 * EQUED = 'R': A := diag(R) * A 00152 * EQUED = 'C': A := A * diag(C) 00153 * EQUED = 'B': A := diag(R) * A * diag(C). 00154 * 00155 * LDAB (input) INTEGER 00156 * The leading dimension of the array AB. LDAB >= KL+KU+1. 00157 * 00158 * AFB (input or output) REAL array, dimension (LDAFB,N) 00159 * If FACT = 'F', then AFB is an input argument and on entry 00160 * contains details of the LU factorization of the band matrix 00161 * A, as computed by SGBTRF. U is stored as an upper triangular 00162 * band matrix with KL+KU superdiagonals in rows 1 to KL+KU+1, 00163 * and the multipliers used during the factorization are stored 00164 * in rows KL+KU+2 to 2*KL+KU+1. If EQUED .ne. 'N', then AFB is 00165 * the factored form of the equilibrated matrix A. 00166 * 00167 * If FACT = 'N', then AF is an output argument and on exit 00168 * returns the factors L and U from the factorization A = P*L*U 00169 * of the original matrix A. 00170 * 00171 * If FACT = 'E', then AF is an output argument and on exit 00172 * returns the factors L and U from the factorization A = P*L*U 00173 * of the equilibrated matrix A (see the description of A for 00174 * the form of the equilibrated matrix). 00175 * 00176 * LDAFB (input) INTEGER 00177 * The leading dimension of the array AFB. LDAFB >= 2*KL+KU+1. 00178 * 00179 * IPIV (input or output) INTEGER array, dimension (N) 00180 * If FACT = 'F', then IPIV is an input argument and on entry 00181 * contains the pivot indices from the factorization A = P*L*U 00182 * as computed by SGETRF; row i of the matrix was interchanged 00183 * with row IPIV(i). 00184 * 00185 * If FACT = 'N', then IPIV is an output argument and on exit 00186 * contains the pivot indices from the factorization A = P*L*U 00187 * of the original matrix A. 00188 * 00189 * If FACT = 'E', then IPIV is an output argument and on exit 00190 * contains the pivot indices from the factorization A = P*L*U 00191 * of the equilibrated matrix A. 00192 * 00193 * EQUED (input or output) CHARACTER*1 00194 * Specifies the form of equilibration that was done. 00195 * = 'N': No equilibration (always true if FACT = 'N'). 00196 * = 'R': Row equilibration, i.e., A has been premultiplied by 00197 * diag(R). 00198 * = 'C': Column equilibration, i.e., A has been postmultiplied 00199 * by diag(C). 00200 * = 'B': Both row and column equilibration, i.e., A has been 00201 * replaced by diag(R) * A * diag(C). 00202 * EQUED is an input argument if FACT = 'F'; otherwise, it is an 00203 * output argument. 00204 * 00205 * R (input or output) REAL array, dimension (N) 00206 * The row scale factors for A. If EQUED = 'R' or 'B', A is 00207 * multiplied on the left by diag(R); if EQUED = 'N' or 'C', R 00208 * is not accessed. R is an input argument if FACT = 'F'; 00209 * otherwise, R is an output argument. If FACT = 'F' and 00210 * EQUED = 'R' or 'B', each element of R must be positive. 00211 * If R is output, each element of R is a power of the radix. 00212 * If R is input, each element of R should be a power of the radix 00213 * to ensure a reliable solution and error estimates. Scaling by 00214 * powers of the radix does not cause rounding errors unless the 00215 * result underflows or overflows. Rounding errors during scaling 00216 * lead to refining with a matrix that is not equivalent to the 00217 * input matrix, producing error estimates that may not be 00218 * reliable. 00219 * 00220 * C (input or output) REAL array, dimension (N) 00221 * The column scale factors for A. If EQUED = 'C' or 'B', A is 00222 * multiplied on the right by diag(C); if EQUED = 'N' or 'R', C 00223 * is not accessed. C is an input argument if FACT = 'F'; 00224 * otherwise, C is an output argument. If FACT = 'F' and 00225 * EQUED = 'C' or 'B', each element of C must be positive. 00226 * If C is output, each element of C is a power of the radix. 00227 * If C is input, each element of C should be a power of the radix 00228 * to ensure a reliable solution and error estimates. Scaling by 00229 * powers of the radix does not cause rounding errors unless the 00230 * result underflows or overflows. Rounding errors during scaling 00231 * lead to refining with a matrix that is not equivalent to the 00232 * input matrix, producing error estimates that may not be 00233 * reliable. 00234 * 00235 * B (input/output) REAL array, dimension (LDB,NRHS) 00236 * On entry, the N-by-NRHS right hand side matrix B. 00237 * On exit, 00238 * if EQUED = 'N', B is not modified; 00239 * if TRANS = 'N' and EQUED = 'R' or 'B', B is overwritten by 00240 * diag(R)*B; 00241 * if TRANS = 'T' or 'C' and EQUED = 'C' or 'B', B is 00242 * overwritten by diag(C)*B. 00243 * 00244 * LDB (input) INTEGER 00245 * The leading dimension of the array B. LDB >= max(1,N). 00246 * 00247 * X (output) REAL array, dimension (LDX,NRHS) 00248 * If INFO = 0, the N-by-NRHS solution matrix X to the original 00249 * system of equations. Note that A and B are modified on exit 00250 * if EQUED .ne. 'N', and the solution to the equilibrated system is 00251 * inv(diag(C))*X if TRANS = 'N' and EQUED = 'C' or 'B', or 00252 * inv(diag(R))*X if TRANS = 'T' or 'C' and EQUED = 'R' or 'B'. 00253 * 00254 * LDX (input) INTEGER 00255 * The leading dimension of the array X. LDX >= max(1,N). 00256 * 00257 * RCOND (output) REAL 00258 * Reciprocal scaled condition number. This is an estimate of the 00259 * reciprocal Skeel condition number of the matrix A after 00260 * equilibration (if done). If this is less than the machine 00261 * precision (in particular, if it is zero), the matrix is singular 00262 * to working precision. Note that the error may still be small even 00263 * if this number is very small and the matrix appears ill- 00264 * conditioned. 00265 * 00266 * RPVGRW (output) REAL 00267 * Reciprocal pivot growth. On exit, this contains the reciprocal 00268 * pivot growth factor norm(A)/norm(U). The "max absolute element" 00269 * norm is used. If this is much less than 1, then the stability of 00270 * the LU factorization of the (equilibrated) matrix A could be poor. 00271 * This also means that the solution X, estimated condition numbers, 00272 * and error bounds could be unreliable. If factorization fails with 00273 * 0<INFO<=N, then this contains the reciprocal pivot growth factor 00274 * for the leading INFO columns of A. In SGESVX, this quantity is 00275 * returned in WORK(1). 00276 * 00277 * BERR (output) REAL array, dimension (NRHS) 00278 * Componentwise relative backward error. This is the 00279 * componentwise relative backward error of each solution vector X(j) 00280 * (i.e., the smallest relative change in any element of A or B that 00281 * makes X(j) an exact solution). 00282 * 00283 * N_ERR_BNDS (input) INTEGER 00284 * Number of error bounds to return for each right hand side 00285 * and each type (normwise or componentwise). See ERR_BNDS_NORM and 00286 * ERR_BNDS_COMP below. 00287 * 00288 * ERR_BNDS_NORM (output) REAL array, dimension (NRHS, N_ERR_BNDS) 00289 * For each right-hand side, this array contains information about 00290 * various error bounds and condition numbers corresponding to the 00291 * normwise relative error, which is defined as follows: 00292 * 00293 * Normwise relative error in the ith solution vector: 00294 * max_j (abs(XTRUE(j,i) - X(j,i))) 00295 * ------------------------------ 00296 * max_j abs(X(j,i)) 00297 * 00298 * The array is indexed by the type of error information as described 00299 * below. There currently are up to three pieces of information 00300 * returned. 00301 * 00302 * The first index in ERR_BNDS_NORM(i,:) corresponds to the ith 00303 * right-hand side. 00304 * 00305 * The second index in ERR_BNDS_NORM(:,err) contains the following 00306 * three fields: 00307 * err = 1 "Trust/don't trust" boolean. Trust the answer if the 00308 * reciprocal condition number is less than the threshold 00309 * sqrt(n) * slamch('Epsilon'). 00310 * 00311 * err = 2 "Guaranteed" error bound: The estimated forward error, 00312 * almost certainly within a factor of 10 of the true error 00313 * so long as the next entry is greater than the threshold 00314 * sqrt(n) * slamch('Epsilon'). This error bound should only 00315 * be trusted if the previous boolean is true. 00316 * 00317 * err = 3 Reciprocal condition number: Estimated normwise 00318 * reciprocal condition number. Compared with the threshold 00319 * sqrt(n) * slamch('Epsilon') to determine if the error 00320 * estimate is "guaranteed". These reciprocal condition 00321 * numbers are 1 / (norm(Z^{-1},inf) * norm(Z,inf)) for some 00322 * appropriately scaled matrix Z. 00323 * Let Z = S*A, where S scales each row by a power of the 00324 * radix so all absolute row sums of Z are approximately 1. 00325 * 00326 * See Lapack Working Note 165 for further details and extra 00327 * cautions. 00328 * 00329 * ERR_BNDS_COMP (output) REAL array, dimension (NRHS, N_ERR_BNDS) 00330 * For each right-hand side, this array contains information about 00331 * various error bounds and condition numbers corresponding to the 00332 * componentwise relative error, which is defined as follows: 00333 * 00334 * Componentwise relative error in the ith solution vector: 00335 * abs(XTRUE(j,i) - X(j,i)) 00336 * max_j ---------------------- 00337 * abs(X(j,i)) 00338 * 00339 * The array is indexed by the right-hand side i (on which the 00340 * componentwise relative error depends), and the type of error 00341 * information as described below. There currently are up to three 00342 * pieces of information returned for each right-hand side. If 00343 * componentwise accuracy is not requested (PARAMS(3) = 0.0), then 00344 * ERR_BNDS_COMP is not accessed. If N_ERR_BNDS .LT. 3, then at most 00345 * the first (:,N_ERR_BNDS) entries are returned. 00346 * 00347 * The first index in ERR_BNDS_COMP(i,:) corresponds to the ith 00348 * right-hand side. 00349 * 00350 * The second index in ERR_BNDS_COMP(:,err) contains the following 00351 * three fields: 00352 * err = 1 "Trust/don't trust" boolean. Trust the answer if the 00353 * reciprocal condition number is less than the threshold 00354 * sqrt(n) * slamch('Epsilon'). 00355 * 00356 * err = 2 "Guaranteed" error bound: The estimated forward error, 00357 * almost certainly within a factor of 10 of the true error 00358 * so long as the next entry is greater than the threshold 00359 * sqrt(n) * slamch('Epsilon'). This error bound should only 00360 * be trusted if the previous boolean is true. 00361 * 00362 * err = 3 Reciprocal condition number: Estimated componentwise 00363 * reciprocal condition number. Compared with the threshold 00364 * sqrt(n) * slamch('Epsilon') to determine if the error 00365 * estimate is "guaranteed". These reciprocal condition 00366 * numbers are 1 / (norm(Z^{-1},inf) * norm(Z,inf)) for some 00367 * appropriately scaled matrix Z. 00368 * Let Z = S*(A*diag(x)), where x is the solution for the 00369 * current right-hand side and S scales each row of 00370 * A*diag(x) by a power of the radix so all absolute row 00371 * sums of Z are approximately 1. 00372 * 00373 * See Lapack Working Note 165 for further details and extra 00374 * cautions. 00375 * 00376 * NPARAMS (input) INTEGER 00377 * Specifies the number of parameters set in PARAMS. If .LE. 0, the 00378 * PARAMS array is never referenced and default values are used. 00379 * 00380 * PARAMS (input / output) REAL array, dimension NPARAMS 00381 * Specifies algorithm parameters. If an entry is .LT. 0.0, then 00382 * that entry will be filled with default value used for that 00383 * parameter. Only positions up to NPARAMS are accessed; defaults 00384 * are used for higher-numbered parameters. 00385 * 00386 * PARAMS(LA_LINRX_ITREF_I = 1) : Whether to perform iterative 00387 * refinement or not. 00388 * Default: 1.0 00389 * = 0.0 : No refinement is performed, and no error bounds are 00390 * computed. 00391 * = 1.0 : Use the double-precision refinement algorithm, 00392 * possibly with doubled-single computations if the 00393 * compilation environment does not support DOUBLE 00394 * PRECISION. 00395 * (other values are reserved for future use) 00396 * 00397 * PARAMS(LA_LINRX_ITHRESH_I = 2) : Maximum number of residual 00398 * computations allowed for refinement. 00399 * Default: 10 00400 * Aggressive: Set to 100 to permit convergence using approximate 00401 * factorizations or factorizations other than LU. If 00402 * the factorization uses a technique other than 00403 * Gaussian elimination, the guarantees in 00404 * err_bnds_norm and err_bnds_comp may no longer be 00405 * trustworthy. 00406 * 00407 * PARAMS(LA_LINRX_CWISE_I = 3) : Flag determining if the code 00408 * will attempt to find a solution with small componentwise 00409 * relative error in the double-precision algorithm. Positive 00410 * is true, 0.0 is false. 00411 * Default: 1.0 (attempt componentwise convergence) 00412 * 00413 * WORK (workspace) REAL array, dimension (4*N) 00414 * 00415 * IWORK (workspace) INTEGER array, dimension (N) 00416 * 00417 * INFO (output) INTEGER 00418 * = 0: Successful exit. The solution to every right-hand side is 00419 * guaranteed. 00420 * < 0: If INFO = -i, the i-th argument had an illegal value 00421 * > 0 and <= N: U(INFO,INFO) is exactly zero. The factorization 00422 * has been completed, but the factor U is exactly singular, so 00423 * the solution and error bounds could not be computed. RCOND = 0 00424 * is returned. 00425 * = N+J: The solution corresponding to the Jth right-hand side is 00426 * not guaranteed. The solutions corresponding to other right- 00427 * hand sides K with K > J may not be guaranteed as well, but 00428 * only the first such right-hand side is reported. If a small 00429 * componentwise error is not requested (PARAMS(3) = 0.0) then 00430 * the Jth right-hand side is the first with a normwise error 00431 * bound that is not guaranteed (the smallest J such 00432 * that ERR_BNDS_NORM(J,1) = 0.0). By default (PARAMS(3) = 1.0) 00433 * the Jth right-hand side is the first with either a normwise or 00434 * componentwise error bound that is not guaranteed (the smallest 00435 * J such that either ERR_BNDS_NORM(J,1) = 0.0 or 00436 * ERR_BNDS_COMP(J,1) = 0.0). See the definition of 00437 * ERR_BNDS_NORM(:,1) and ERR_BNDS_COMP(:,1). To get information 00438 * about all of the right-hand sides check ERR_BNDS_NORM or 00439 * ERR_BNDS_COMP. 00440 * 00441 * ================================================================== 00442 * 00443 * .. Parameters .. 00444 REAL ZERO, ONE 00445 PARAMETER ( ZERO = 0.0E+0, ONE = 1.0E+0 ) 00446 INTEGER FINAL_NRM_ERR_I, FINAL_CMP_ERR_I, BERR_I 00447 INTEGER RCOND_I, NRM_RCOND_I, NRM_ERR_I, CMP_RCOND_I 00448 INTEGER CMP_ERR_I, PIV_GROWTH_I 00449 PARAMETER ( FINAL_NRM_ERR_I = 1, FINAL_CMP_ERR_I = 2, 00450 $ BERR_I = 3 ) 00451 PARAMETER ( RCOND_I = 4, NRM_RCOND_I = 5, NRM_ERR_I = 6 ) 00452 PARAMETER ( CMP_RCOND_I = 7, CMP_ERR_I = 8, 00453 $ PIV_GROWTH_I = 9 ) 00454 * .. 00455 * .. Local Scalars .. 00456 LOGICAL COLEQU, EQUIL, NOFACT, NOTRAN, ROWEQU 00457 INTEGER INFEQU, I, J, KL, KU 00458 REAL AMAX, BIGNUM, COLCND, RCMAX, RCMIN, 00459 $ ROWCND, SMLNUM 00460 * .. 00461 * .. External Functions .. 00462 EXTERNAL LSAME, SLAMCH, SLA_GBRPVGRW 00463 LOGICAL LSAME 00464 REAL SLAMCH, SLA_GBRPVGRW 00465 * .. 00466 * .. External Subroutines .. 00467 EXTERNAL SGBEQUB, SGBTRF, SGBTRS, SLACPY, SLAQGB, 00468 $ XERBLA, SLASCL2, SGBRFSX 00469 * .. 00470 * .. Intrinsic Functions .. 00471 INTRINSIC MAX, MIN 00472 * .. 00473 * .. Executable Statements .. 00474 * 00475 INFO = 0 00476 NOFACT = LSAME( FACT, 'N' ) 00477 EQUIL = LSAME( FACT, 'E' ) 00478 NOTRAN = LSAME( TRANS, 'N' ) 00479 SMLNUM = SLAMCH( 'Safe minimum' ) 00480 BIGNUM = ONE / SMLNUM 00481 IF( NOFACT .OR. EQUIL ) THEN 00482 EQUED = 'N' 00483 ROWEQU = .FALSE. 00484 COLEQU = .FALSE. 00485 ELSE 00486 ROWEQU = LSAME( EQUED, 'R' ) .OR. LSAME( EQUED, 'B' ) 00487 COLEQU = LSAME( EQUED, 'C' ) .OR. LSAME( EQUED, 'B' ) 00488 END IF 00489 * 00490 * Default is failure. If an input parameter is wrong or 00491 * factorization fails, make everything look horrible. Only the 00492 * pivot growth is set here, the rest is initialized in SGBRFSX. 00493 * 00494 RPVGRW = ZERO 00495 * 00496 * Test the input parameters. PARAMS is not tested until SGBRFSX. 00497 * 00498 IF( .NOT.NOFACT .AND. .NOT.EQUIL .AND. .NOT. 00499 $ LSAME( FACT, 'F' ) ) THEN 00500 INFO = -1 00501 ELSE IF( .NOT.NOTRAN .AND. .NOT.LSAME( TRANS, 'T' ) .AND. .NOT. 00502 $ LSAME( TRANS, 'C' ) ) THEN 00503 INFO = -2 00504 ELSE IF( N.LT.0 ) THEN 00505 INFO = -3 00506 ELSE IF( KL.LT.0 ) THEN 00507 INFO = -4 00508 ELSE IF( KU.LT.0 ) THEN 00509 INFO = -5 00510 ELSE IF( NRHS.LT.0 ) THEN 00511 INFO = -6 00512 ELSE IF( LDAB.LT.KL+KU+1 ) THEN 00513 INFO = -8 00514 ELSE IF( LDAFB.LT.2*KL+KU+1 ) THEN 00515 INFO = -10 00516 ELSE IF( LSAME( FACT, 'F' ) .AND. .NOT. 00517 $ ( ROWEQU .OR. COLEQU .OR. LSAME( EQUED, 'N' ) ) ) THEN 00518 INFO = -12 00519 ELSE 00520 IF( ROWEQU ) THEN 00521 RCMIN = BIGNUM 00522 RCMAX = ZERO 00523 DO 10 J = 1, N 00524 RCMIN = MIN( RCMIN, R( J ) ) 00525 RCMAX = MAX( RCMAX, R( J ) ) 00526 10 CONTINUE 00527 IF( RCMIN.LE.ZERO ) THEN 00528 INFO = -13 00529 ELSE IF( N.GT.0 ) THEN 00530 ROWCND = MAX( RCMIN, SMLNUM ) / MIN( RCMAX, BIGNUM ) 00531 ELSE 00532 ROWCND = ONE 00533 END IF 00534 END IF 00535 IF( COLEQU .AND. INFO.EQ.0 ) THEN 00536 RCMIN = BIGNUM 00537 RCMAX = ZERO 00538 DO 20 J = 1, N 00539 RCMIN = MIN( RCMIN, C( J ) ) 00540 RCMAX = MAX( RCMAX, C( J ) ) 00541 20 CONTINUE 00542 IF( RCMIN.LE.ZERO ) THEN 00543 INFO = -14 00544 ELSE IF( N.GT.0 ) THEN 00545 COLCND = MAX( RCMIN, SMLNUM ) / MIN( RCMAX, BIGNUM ) 00546 ELSE 00547 COLCND = ONE 00548 END IF 00549 END IF 00550 IF( INFO.EQ.0 ) THEN 00551 IF( LDB.LT.MAX( 1, N ) ) THEN 00552 INFO = -15 00553 ELSE IF( LDX.LT.MAX( 1, N ) ) THEN 00554 INFO = -16 00555 END IF 00556 END IF 00557 END IF 00558 * 00559 IF( INFO.NE.0 ) THEN 00560 CALL XERBLA( 'SGBSVXX', -INFO ) 00561 RETURN 00562 END IF 00563 * 00564 IF( EQUIL ) THEN 00565 * 00566 * Compute row and column scalings to equilibrate the matrix A. 00567 * 00568 CALL SGBEQUB( N, N, KL, KU, AB, LDAB, R, C, ROWCND, COLCND, 00569 $ AMAX, INFEQU ) 00570 IF( INFEQU.EQ.0 ) THEN 00571 * 00572 * Equilibrate the matrix. 00573 * 00574 CALL SLAQGB( N, N, KL, KU, AB, LDAB, R, C, ROWCND, COLCND, 00575 $ AMAX, EQUED ) 00576 ROWEQU = LSAME( EQUED, 'R' ) .OR. LSAME( EQUED, 'B' ) 00577 COLEQU = LSAME( EQUED, 'C' ) .OR. LSAME( EQUED, 'B' ) 00578 END IF 00579 * 00580 * If the scaling factors are not applied, set them to 1.0. 00581 * 00582 IF ( .NOT.ROWEQU ) THEN 00583 DO J = 1, N 00584 R( J ) = 1.0 00585 END DO 00586 END IF 00587 IF ( .NOT.COLEQU ) THEN 00588 DO J = 1, N 00589 C( J ) = 1.0 00590 END DO 00591 END IF 00592 END IF 00593 * 00594 * Scale the right hand side. 00595 * 00596 IF( NOTRAN ) THEN 00597 IF( ROWEQU ) CALL SLASCL2(N, NRHS, R, B, LDB) 00598 ELSE 00599 IF( COLEQU ) CALL SLASCL2(N, NRHS, C, B, LDB) 00600 END IF 00601 * 00602 IF( NOFACT .OR. EQUIL ) THEN 00603 * 00604 * Compute the LU factorization of A. 00605 * 00606 DO 40, J = 1, N 00607 DO 30, I = KL+1, 2*KL+KU+1 00608 AFB( I, J ) = AB( I-KL, J ) 00609 30 CONTINUE 00610 40 CONTINUE 00611 CALL SGBTRF( N, N, KL, KU, AFB, LDAFB, IPIV, INFO ) 00612 * 00613 * Return if INFO is non-zero. 00614 * 00615 IF( INFO.GT.0 ) THEN 00616 * 00617 * Pivot in column INFO is exactly 0 00618 * Compute the reciprocal pivot growth factor of the 00619 * leading rank-deficient INFO columns of A. 00620 * 00621 RPVGRW = SLA_GBRPVGRW( N, KL, KU, INFO, AB, LDAB, AFB, 00622 $ LDAFB ) 00623 RETURN 00624 END IF 00625 END IF 00626 * 00627 * Compute the reciprocal pivot growth factor RPVGRW. 00628 * 00629 RPVGRW = SLA_GBRPVGRW( N, KL, KU, N, AB, LDAB, AFB, LDAFB ) 00630 * 00631 * Compute the solution matrix X. 00632 * 00633 CALL SLACPY( 'Full', N, NRHS, B, LDB, X, LDX ) 00634 CALL SGBTRS( TRANS, N, KL, KU, NRHS, AFB, LDAFB, IPIV, X, LDX, 00635 $ INFO ) 00636 * 00637 * Use iterative refinement to improve the computed solution and 00638 * compute error bounds and backward error estimates for it. 00639 * 00640 CALL SGBRFSX( TRANS, EQUED, N, KL, KU, NRHS, AB, LDAB, AFB, LDAFB, 00641 $ IPIV, R, C, B, LDB, X, LDX, RCOND, BERR, 00642 $ N_ERR_BNDS, ERR_BNDS_NORM, ERR_BNDS_COMP, NPARAMS, PARAMS, 00643 $ WORK, IWORK, INFO ) 00644 * 00645 * Scale solutions. 00646 * 00647 IF ( COLEQU .AND. NOTRAN ) THEN 00648 CALL SLASCL2 ( N, NRHS, C, X, LDX ) 00649 ELSE IF ( ROWEQU .AND. .NOT.NOTRAN ) THEN 00650 CALL SLASCL2 ( N, NRHS, R, X, LDX ) 00651 END IF 00652 * 00653 RETURN 00654 * 00655 * End of SGBSVXX 00656 * 00657 END
1.7.3 
